Browsing by Author "Lu, Hao-Chun"

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A note on "Reducing the number of binary variables in cutting stock problems"
(2014-02-01)
Lu, Hao-Chun
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Ko, Yu-Chien
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Huang, Yao-Huei
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資訊管理與財務金融系註：原資管所+財金所
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Department of Information Management and Finance
This study proposes a deterministic model to solve the two-dimensional cutting stock problem (2DCSP) using a much smaller number of binary variables and thereby reducing the complexity of 2DCSP. Expressing a 2DCSP with stocks and cutting rectangles requires binary variables in the traditional model. In contrast, the proposed model uses binary variables to express the 2DCSP. Experimental results showed that the proposed model is more efficient than the existing model.
A Superior Representation Method for Piecewise Linear Functions
(2009-03-01)
Li, Han-Lin
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Lu, Hao-Chun
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Huang, Chia-Hui
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Hu, Nian-Ze
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資訊管理與財務金融系註：原資管所+財金所
Many nonlinear programs can be piecewisely linearized by adding extra binary variables. For the last four decades, several techniques of formulating a piecewise linear function have been developed. By expressing a piecewise linear function with m+1 break points, the current method requires us to use m additional binary variables and 4m constraints, which causes heavy computation when m is large. This study proposes a superior way of expressing the same piecewise linear function, where only [log(2)m] binary variables and 8+8 [log(2)m] additive constraints are used. Various numerical experiments demonstrate that the proposed method is more computationally efficient than current methods.
An integrated algorithm for cutting stock problems in the thin-film transistor liquid crystal display industry
(2013-04-01)
Lu, Hao-Chun
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Huang, Yao-Huei
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Tseng, Kuo-An
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
The cutting stock problem (CSP) is a critical issue in the manufacturing of thin film transistor liquid crystal display (TFT-LCD) products. Two manufacturing processes are utilized in this industry: (1) various TFT-LCD plates are cut from a glass substrate based on cutting patterns, and (2) the number of glass substrates required to satisfy customer requirements is minimized. The current algorithm used to select the cutting pattern is defined as a mixed integer program (MIP). Although the current MIP method yields an optimal solution, but the computation time is unacceptable when the problem scale is large. To accelerate the computation and improve the current method, this study proposes an integrated algorithm that incorporates a genetic algorithm, a corner arrangement method, and a production plan model to solve CSPs in the TFT-LCD industry. The results of numerical experiments demonstrate that the proposed algorithm is significantly more efficient than the current method, especially when applied to large-scale problems. (C) 2013 Elsevier Ltd. All rights reserved.
An Optimal Classification Method for Biological and Medical Data
(2012)
Huang, Yao-Huei
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Ko, Yu-Chien
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Lu, Hao-Chun
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
This paper proposes a union of hyperspheres by the mixed-integer nonlinear program to classify biological and medical datasets. A classifying program with nonlinear terms uses piecewise linearization technique to obtain a global optimum. The numerical examples illustrate that the proposed method can obtain the global optimum more effectively than current methods.
Convex relaxation for solving posynomial programs
(2010-01-01)
Lu, Hao-Chun
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Li, Han-Lin
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Gounaris, Chrysanthos E.
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Floudas, Christodoulos A.
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資訊管理與財務金融系註：原資管所+財金所
Convex underestimation techniques for nonlinear functions are an essential part of global optimization. These techniques usually involve the addition of new variables and constraints. In the case of posynomial functions x(1)(alpha 1)x(2)(alpha 2) ... x(n)(alpha n), logarithmic transformations (Maranas and Floudas, Comput. Chem. Eng. 21: 351-370, 1997) are typically used. This study develops an effective method for finding a tight relaxation of a posynomial function by introducing variables y(j) and positive parameters beta(j), for all alpha(j) > 0, such that y(j) = x(j)(-beta j). By specifying beta(j) carefully, we can find a tighter underestimation than the current methods.
Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables
(2009-05-01)
Li, Han-Lin
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Lu, Hao-Chun
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Many optimization problems are formulated as generalized geometric programming (GGP) containing signomial terms f(X) . g(Y), where X and Y are continuous and discrete free-sign vectors, respectively. By effectively convexifying f(X) and linearizing g(Y), this study globally solves a GGP with a lower number of binary variables than are used in current GGP methods. Numerical experiments demonstrate the computational efficiency of the proposed method.